Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
page |< < of 145 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="063/01/070.jpg"/>
                <emph type="italics"/>
              ab
                <emph.end type="italics"/>
              linea hypomochlij, &
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              ad eam perpendicularis:
                <expan abbr="eritq;">eritque</expan>
              ex
                <lb/>
              iam demonſtratis
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              grauitas mouens, &
                <emph type="italics"/>
              ag
                <emph.end type="italics"/>
              plaga eiuſdem
                <lb/>
              centri. </s>
              <s>Et quia plaga eſt in lineâ
                <emph type="italics"/>
              af;
                <emph.end type="italics"/>
              erit motus reflexus in
                <lb/>
              eadem lineâ
                <emph type="italics"/>
              af.
                <emph.end type="italics"/>
              quòd ſi ergo fiat ut
                <emph type="italics"/>
              ag
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              gf,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              ah
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              ak,
                <emph.end type="italics"/>
              erit
                <lb/>
              motus medius in
                <emph type="italics"/>
              ai,
                <emph.end type="italics"/>
              & angulus reflexûs
                <emph type="italics"/>
              iak:
                <emph.end type="italics"/>
              quem dico æqua­
                <lb/>
              lem angulo incidentiæ
                <emph type="italics"/>
              oab.
                <emph.end type="italics"/>
              Quia enim angulus
                <emph type="italics"/>
              oab
                <emph.end type="italics"/>
              eſt æ­
                <lb/>
              qualis angulo
                <emph type="italics"/>
              afg,
                <emph.end type="italics"/>
              propterea quòd
                <expan abbr="uterq;">uterque</expan>
              ſit complementum
                <lb/>
              anguli
                <emph type="italics"/>
              fag:
                <emph.end type="italics"/>
              angulo autem
                <emph type="italics"/>
              gfa
                <emph.end type="italics"/>
              æquatur angulus
                <emph type="italics"/>
              iak,
                <emph.end type="italics"/>
              quòd ſi­
                <lb/>
              milia ſint triangula
                <emph type="italics"/>
              agf. iak:
                <emph.end type="italics"/>
              erit
                <expan abbr="quoq;">quoque</expan>
              angulo
                <emph type="italics"/>
              oab
                <emph.end type="italics"/>
              idem
                <lb/>
              angulus
                <emph type="italics"/>
              iak
                <emph.end type="italics"/>
              æqualis. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA XIII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Motus Pentagoni ſecans obliquè planum, ſi latus, quod tangit pla­
                <lb/>
              num eidem ſit parallelum, ad angulos inæquales reſle­
                <lb/>
              ctit.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Motus Pentagoni
                <emph type="italics"/>
              abcde
                <emph.end type="italics"/>
              incidat obliquè plano
                <emph type="italics"/>
              ſt
                <emph.end type="italics"/>
              habens la­
                <lb/>
              tus
                <emph type="italics"/>
              ae,
                <emph.end type="italics"/>
              quod tangit planum, eidem parallelum: dico hunc mo­
                <lb/>
              tum reflecti ad angulos inæquales. </s>
              <s>Excitetur linea hypomo­
                <lb/>
              chlij
                <emph type="italics"/>
              en,
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              ad eam perpendicularis:
                <expan abbr="eritq;">eritque</expan>
              grauitas tota
                <expan abbr="qua-dratũ">qua­
                  <lb/>
                dratum</expan>
                <emph type="italics"/>
              fh;
                <emph.end type="italics"/>
              grauitas autem mo vens quadratum
                <emph type="italics"/>
              fg.
                <emph.end type="italics"/>
              dividatur bi­
                <lb/>
              fariam linea
                <emph type="italics"/>
              hf
                <emph.end type="italics"/>
              in
                <emph type="italics"/>
              p;
                <emph.end type="italics"/>
                <expan abbr="eoq;">eoque</expan>
              centro circulus deſcribatur
                <emph type="italics"/>
              hif.
                <emph.end type="italics"/>
                <lb/>
              Quòd ſi ergo ſumatur chorda
                <emph type="italics"/>
              fi
                <emph.end type="italics"/>
              æqualis
                <emph type="italics"/>
              fg;
                <emph.end type="italics"/>
              erit chorda re­
                <lb/>
              liqua
                <emph type="italics"/>
              hi;
                <emph.end type="italics"/>
                <expan abbr="atq;">atque</expan>
              huius quadratum dabit plagam. </s>
              <s>Et quia plaga
                <lb/>
              fit per lineas
                <emph type="italics"/>
              fa. fh. fe:
                <emph.end type="italics"/>
              erit per 5 theor: huius motus reflexus
                <lb/>
              in lineâ
                <emph type="italics"/>
              fc,
                <emph.end type="italics"/>
              & motus centri in lineâ
                <emph type="italics"/>
              fm
                <emph.end type="italics"/>
              eidem plano parallelâ. </s>
              <lb/>
              <s>Si ergo fiat ut
                <emph type="italics"/>
              fi
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              ih,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              fm
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              fl;
                <emph.end type="italics"/>
              erit motus medius
                <emph type="italics"/>
              fk,
                <emph.end type="italics"/>
              &
                <lb/>
              angulus reflexionis
                <emph type="italics"/>
              kfm;
                <emph.end type="italics"/>
              quem dico inæqualem angulo in­
                <lb/>
              cidentiæ
                <emph type="italics"/>
              hen.
                <emph.end type="italics"/>
              Quia enim angulus
                <emph type="italics"/>
              ahi
                <emph.end type="italics"/>
              externus eſt maior </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum